Question

The line segment determined by A(4,7) and B(2, 9) along <0, –2>
The endpoints of the image
…?

Answer 1

The endpoints of the image are $A'(x,y) = (4,5)$ and $B'(x,y) = (2,7)$, respectively.

Note - The statement is incomplete. Complete description is shown below:

The line segment determined by $A(4,7)$ and $B(2,9)$ is translated along $\langle 0, -2\rangle$. Determine the endpoints of the image of the line segment AB.

Vectorially speaking, the translation of a point is defined by this formula:

$P'(x,y) = P(x,y) + T(x,y)$ (1)

Where:

• $P(x,y)$ - Original point.
• $P'(x,y)$ - Resulting point.
• $T(x,y)$ - Translation.

Now we proceed to calculate the endpoints of the image:

Point A

$A'(x,y) = A(x,y) + T(x,y)$

$A'(x,y) = (4,7) + (0,-2)$

$A'(x,y) = (4,5)$

Point B

$B'(x,y) = B(x,y) + T(x,y)$

$B'(x,y) = (2,9) + (0,-2)$

$B'(x,y) = (2,7)$

The endpoints of the image are $A'(x,y) = (4,5)$ and $B'(x,y) = (2,7)$, respectively.

We kindly invite to see this question on translations: https://brainly.com/question/12463306